Moore’s Law continues to apply to Code_Aster!
by O.Boiteau, EDF R&D / SINETICS
Even if from the hardware point of view the performance increase predicted by Moore’s law starts to falter, significant accelerations can still be noticed after each release of Code_Aster, in different parts of the code which directly benefit to the studies.
Thus, the dimensioning stage of large studies, that is the resolution of linear systems of equations, recently took advantage of advances in the MUMPS product [1] which is used very often, especially in parallel. With Code_Aster v13.1, by leveraging two new features of this external tool - an additional level of parallelism associated with algorithmic compressions - these large studies may see their computing time reduced by at least 50% (see Figures 1 and 2). This is achieved without noticeable impact on the scope of use, the accuracy or reliability of the calculations and … contrary to Moore’s law, without changing the machine or the number of allocated nodes !
Towards hybrid parallelism
Often, because of memory limitations, the calculation is distributed across multiple computer nodes (using "MPI" parallelism) which leads to a waste of computing power: for example, on the centralized server Aster5, one usually operates around ten cores per node while … 24 are available. An additional level of parallelism ("thread-based" parallelism) is now automatically activated within each MPI process by ASTK, the calculations therefore take better advantage of the resources available, contributing to the reduction of computation time.
Compress and conquer
This "computer-based" acceleration can be combined with another, rather "algorithmic" relying on ’block low-rank’ compressions [2]. Similarly to MP3 or ZIP formats, these compressions enable the decrease in memory and time of MUMPS costly steps, with little noticeable loss. This approximation does not generally change the accuracy and behaviour of mechanical calculations (particular in non-linear analyses).
Code_Aster users hereby reap the fruits of the labour of the EDF-MUMPS partnership, initiated almost five years with the PhD of Clement Weisbecker [3]. These highly innovative thesis works were as a matter of fact rewarded with the Leopold Escande Leopold price in 2014 [4].
|
|
| Figure 1 : Temps de calcul et accélérations sur cas-test de performance PERF008 | Figure 2 : Temps de calcul et accélérations sur cas-test de performance PERF009 |
A consortium for the future
Finally, let us say that apart from EDF, many other industrial companies, software vendors and academic teams rely on MUMPS (IRIT, INRIA, CERFACS, CNRS, Michelin, Total, SAMCEF, LS-DYNA, ESI, … ALTAIR) and to effectively support its development and sustainment, they have regrouped together in a consortium. EDF has played a significant part in its creation and the launch meeting of the new entity was held in Lab EDF Clamart in late 2015 [5].
[1] http://graal.ens-lyon.fr/MUMPS/.
[2] P.Amestoy, C.Ashcraft, O.Boiteau, A.Buttari, J.Y.L’Excellent et C.Weisbecker. Improving multifrontal methods by means of block low-rank representations. SIAM Journal on Scientific Computing 37(3), A1451-1474.
[3] http://www.theses.fr/2013INPT0134.
[4] http://ethesis.inp-toulouse.fr/view/prix/Prix_L=E9opold_Escande_2013.html.
[5] https://mumps-consortium.org/